| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,1,1,3,3,0,0,1,1,1,0,1,-1,-1,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.1354'] |
| Arrow polynomial of the knot is: -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.323', '6.380', '6.444', '6.472', '6.523', '6.579', '6.592', '6.595', '6.609', '6.614', '6.620', '6.644', '6.648', '6.669', '6.671', '6.681', '6.693', '6.724', '6.725', '6.757', '6.766', '6.785', '6.786', '6.797', '6.798', '6.816', '6.833', '6.972', '6.978', '6.1056', '6.1064', '6.1066', '6.1087', '6.1094', '6.1273', '6.1277', '6.1282', '6.1295', '6.1300', '6.1313', '6.1344', '6.1353', '6.1354'] |
| Outer characteristic polynomial of the knot is: t^7+46t^5+47t^3+6t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1354'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**4*K2**2 + 1120*K1**4*K2 - 2384*K1**4 + 448*K1**3*K2*K3 + 32*K1**3*K3*K4 - 128*K1**3*K3 + 736*K1**2*K2**3 - 5168*K1**2*K2**2 - 512*K1**2*K2*K4 + 6544*K1**2*K2 - 304*K1**2*K3**2 - 96*K1**2*K4**2 - 3316*K1**2 + 96*K1*K2**3*K3 - 768*K1*K2**2*K3 - 64*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 4552*K1*K2*K3 + 760*K1*K3*K4 + 104*K1*K4*K5 - 456*K2**4 - 96*K2**2*K3**2 - 8*K2**2*K4**2 + 760*K2**2*K4 - 2782*K2**2 + 136*K2*K3*K5 + 8*K2*K4*K6 - 1100*K3**2 - 358*K4**2 - 48*K5**2 - 2*K6**2 + 2836 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1354'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16523', 'vk6.16616', 'vk6.17511', 'vk6.17568', 'vk6.18869', 'vk6.18947', 'vk6.19203', 'vk6.19498', 'vk6.23051', 'vk6.24108', 'vk6.25497', 'vk6.25572', 'vk6.26013', 'vk6.26399', 'vk6.34926', 'vk6.35040', 'vk6.36298', 'vk6.36367', 'vk6.37602', 'vk6.37691', 'vk6.42500', 'vk6.42612', 'vk6.43477', 'vk6.44602', 'vk6.54766', 'vk6.54859', 'vk6.56434', 'vk6.56563', 'vk6.59290', 'vk6.60184', 'vk6.66098', 'vk6.66140'] |
| The R3 orbit of minmal crossing diagrams contains: |
| The diagrammatic symmetry type of this knot is c. |
| The reverse -K is |
| The mirror image K* is |
| The reversed mirror image -K* is |
| The fillings (up to the first 10) associated to the algebraic genus: |
| Or click here to check the fillings |
| invariant | value |
|---|---|
| Gauss code | O1O2O3U2O4O5U1U4U3O6U5U6 |
| R3 orbit | {'O1O2O3U2O4O5U1U4U3O6U5U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5O4U1U6U3O5O6U2 |
| Gauss code of K* | O1O2O3U4O5O4U1U6U3O6U2U5 |
| Gauss code of -K* | O1O2O3U4U2O5U1U5U3O6O4U6 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 3 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -3 -1 1 0 2 1],[ 3 0 0 3 1 3 1],[ 1 0 0 1 0 1 0],[-1 -3 -1 0 0 2 1],[ 0 -1 0 0 0 1 1],[-2 -3 -1 -2 -1 0 1],[-1 -1 0 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 1 -2 -1 -1 -3],[-1 -1 0 -1 -1 0 -1],[-1 2 1 0 0 -1 -3],[ 0 1 1 0 0 0 -1],[ 1 1 0 1 0 0 0],[ 3 3 1 3 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,-1,2,1,1,3,1,1,0,1,0,1,3,0,1,0] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,1,1,3,3,0,0,1,1,1,0,1,-1,-1,2] |
| Phi of -K | [-3,-1,0,1,1,2,2,2,1,3,2,1,1,2,2,1,0,1,-1,-1,2] |
| Phi of K* | [-2,-1,-1,0,1,3,-1,2,1,2,2,1,1,1,1,0,2,3,1,2,2] |
| Phi of -K* | [-3,-1,0,1,1,2,0,1,1,3,3,0,0,1,1,1,0,1,-1,-1,2] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 4z^2+23z+31 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2+23w^2z+31w |
| Inner characteristic polynomial | t^6+30t^4+18t^2+1 |
| Outer characteristic polynomial | t^7+46t^5+47t^3+6t |
| Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | -448*K1**4*K2**2 + 1120*K1**4*K2 - 2384*K1**4 + 448*K1**3*K2*K3 + 32*K1**3*K3*K4 - 128*K1**3*K3 + 736*K1**2*K2**3 - 5168*K1**2*K2**2 - 512*K1**2*K2*K4 + 6544*K1**2*K2 - 304*K1**2*K3**2 - 96*K1**2*K4**2 - 3316*K1**2 + 96*K1*K2**3*K3 - 768*K1*K2**2*K3 - 64*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 4552*K1*K2*K3 + 760*K1*K3*K4 + 104*K1*K4*K5 - 456*K2**4 - 96*K2**2*K3**2 - 8*K2**2*K4**2 + 760*K2**2*K4 - 2782*K2**2 + 136*K2*K3*K5 + 8*K2*K4*K6 - 1100*K3**2 - 358*K4**2 - 48*K5**2 - 2*K6**2 + 2836 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {4, 5}, {1, 2}]] |
| If K is slice | False |